Introduction In the common textbook presentation of quantum mechanics the observables of a quantum system are represented by selfadjoint operators, or, equivalently , by spectral measures. The origin of this point of view dates back to the very beginning of quantum theory. Its rigorous mathematical formulation is mainly due to von Neumann [53], and, for a more recent and complete review, we ref...

Let α1, α2, . . . , αn, β1, β2, . . . , βn be strictly positive reals with α1 +α2 + · · ·+αn = β1 + β2 + · · ·+ βn = s. In this paper, the inequality |||Aα1Bβ1Aα2 · · ·AαnBβn ||| ≤ |||AB|||s when A and B are positive-definite matrices is studied. Related questions are also studied.

We study the moduli space of instantons on a simply connected positive definite four manifold by analyzing the classifying map of the index bundle of a family of Dirac operators parametrized by the moduli space. As applications we compute the cohomology ring for the charge 2 moduli space in the rank stable limit.

in order to obtain information about the rate of convergence and the saturation properties of the sequence (Ln). The above formula is called Voronovskaya’s formula for the sequence (Ln)n≥1. This paper is devoted to establishing a Voronovskaya-type formula for the sequence of positive linear operators introduced in [1], which approximate continuous functions of exponential order. To obtain the o...

We examine the longstanding problem of introducing a time observable in Quantum Mechanics; using the formalism of positive-operator-valued measures we show how to define such an observable in a natural way and we discuss some consequences.

We consider a positive linear operator An defined on the space of continuous functions having exponential growth at infinity. We give an asymptotic estimate of the remainder. The results obtained are extended to the case of two variables.

Let Ai (i = 1,2, · · · ,k) be bounded linear operators on a Hilbert space. This paper aims to show a characterization of operator order Ak Ak−1 · · · A2 A1 > 0 in terms of operator inequalities. Afterwards, an application of the characterization is given to operator equalities due to Douglas’s majorization and factorization theorem. Mathematics subject classification (2010): 47A63.

A quantum version of the Monty Hall problem, based upon the Positive Operator Valued Measures (POVM) formalism, is proposed. It is shown that basic normalization and symmetry arguments lead univocally to the associated POVM elements, and that the classical probabilities associated with the Monty Hall scenario are recovered for a natural choice of the measurement operators.

Semantics and Memory Semantic Composition Inspired by Quantum Measurement. . . . . . . . . . . . . . 41 William Blacoe Expansion-by-Analogy: A Vector Symbolic Approach to Semantic Search . . . 54 Trevor Cohen, Dominic Widdows, and Thomas Rindflesch Subadditivity of Episodic Memory States: A Complementarity Approach . . . . 67 Jacob Denolf A Vector Field Approach to Lexical Semantics. . . . . . ...